Subgroups — C₂×D₁₂ #234

Order 48.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₄	—	3	1	no	maximal, Sylow
5	C₂²×C₃	C₂²	1	1	yes	characteristic
6	C₂×D₃	—	2	4	no	—
7	C₂×D₃	C₂²	1	4	yes	complemented
8	C₃×C₄	C₂²	1	2	yes	complemented
9	C₂³	—	3	2	no	—
10	D₄	—	3	4	no	—
11	C₂×C₄	D₃	1	1	yes	characteristic, complemented
12	C₂×C₃	D₄	1	2	yes	complemented
13	C₂×C₃	C₂³	1	1	yes	characteristic
14	D₃	—	2	4	no	—
15	C₂²	—	3	4	no	—
16	C₂²	—	6	4	no	—
17	C₂²	C₂×D₃	1	1	yes	characteristic
18	C₄	C₂×D₃	1	2	yes	complemented
19	C₃	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
20	C₂	—	6	4	no	—
21	C₂	D₁₂	1	2	yes	direct product factor
22	C₂	C₂²×D₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.